The performance of stochastic Taylor methods and derivative-free method to approximate the solutions of stochastic delay differential equations
This paper is devoted to investigate the performance of stochastic Taylor methods and derivative-free method to approximate the solutions of stochastic delay differential equations (SDDEs) in population dynamics. The corresponding deterministic models of population dynamics follow the generalised of...
| Main Authors: | , , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
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AIP Publishing
2019
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| Subjects: | |
| Online Access: | http://umpir.ump.edu.my/id/eprint/27730/ http://umpir.ump.edu.my/id/eprint/27730/1/The%20performance%20of%20stochastic%20Taylor%20methods%20and%20derivative-free.pdf |
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| author | Norhayati, Rosli Noor Julailah, Abd Mutalib Noor Amalina Nisa, Ariffin Mazma Syahidatul Ayuni, Mazlan |
| author_facet | Norhayati, Rosli Noor Julailah, Abd Mutalib Noor Amalina Nisa, Ariffin Mazma Syahidatul Ayuni, Mazlan |
| author_sort | Norhayati, Rosli |
| building | UMP Institutional Repository |
| collection | Online Access |
| description | This paper is devoted to investigate the performance of stochastic Taylor methods and derivative-free method to approximate the solutions of stochastic delay differential equations (SDDEs) in population dynamics. The corresponding deterministic models of population dynamics follow the generalised of Verhults laws. Stochastic Taylor methods for SDDEs are developed by truncating the stochastic Taylor series expansion with time delay at certain order. As the order increasing, the method is proving theoretically will provide better solutions for SDDEs. However, the difficulty arises in implementing the stochastic Taylor methods as one needs to find the partial derivative of drift and diffusion functions. It is then natural to look for derivative-free method. This paper demonstrates the performance of the existing stochastic Taylor methods of Euler Maruyama and Milstein scheme and the derivative-free method of 1.0 order of convergence in approximating the solutions of SDDEs models under Verhutls laws. Numerical experiments are conducted to demonstrate the performance of the corresponding methods in approximating the solutions of SDDEs. |
| first_indexed | 2025-11-15T02:48:05Z |
| format | Conference or Workshop Item |
| id | ump-27730 |
| institution | Universiti Malaysia Pahang |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T02:48:05Z |
| publishDate | 2019 |
| publisher | AIP Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | ump-277302020-06-18T02:31:39Z http://umpir.ump.edu.my/id/eprint/27730/ The performance of stochastic Taylor methods and derivative-free method to approximate the solutions of stochastic delay differential equations Norhayati, Rosli Noor Julailah, Abd Mutalib Noor Amalina Nisa, Ariffin Mazma Syahidatul Ayuni, Mazlan T Technology (General) TA Engineering (General). Civil engineering (General) This paper is devoted to investigate the performance of stochastic Taylor methods and derivative-free method to approximate the solutions of stochastic delay differential equations (SDDEs) in population dynamics. The corresponding deterministic models of population dynamics follow the generalised of Verhults laws. Stochastic Taylor methods for SDDEs are developed by truncating the stochastic Taylor series expansion with time delay at certain order. As the order increasing, the method is proving theoretically will provide better solutions for SDDEs. However, the difficulty arises in implementing the stochastic Taylor methods as one needs to find the partial derivative of drift and diffusion functions. It is then natural to look for derivative-free method. This paper demonstrates the performance of the existing stochastic Taylor methods of Euler Maruyama and Milstein scheme and the derivative-free method of 1.0 order of convergence in approximating the solutions of SDDEs models under Verhutls laws. Numerical experiments are conducted to demonstrate the performance of the corresponding methods in approximating the solutions of SDDEs. AIP Publishing 2019-12-04 Conference or Workshop Item PeerReviewed pdf en http://umpir.ump.edu.my/id/eprint/27730/1/The%20performance%20of%20stochastic%20Taylor%20methods%20and%20derivative-free.pdf Norhayati, Rosli and Noor Julailah, Abd Mutalib and Noor Amalina Nisa, Ariffin and Mazma Syahidatul Ayuni, Mazlan (2019) The performance of stochastic Taylor methods and derivative-free method to approximate the solutions of stochastic delay differential equations. In: AIP Conference Proceedings; 1st International Conference on Mathematical Sciences and Technology 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation, MathTech 2018 , 10 - 12 December 2018 , Penang, Malaysia. , 2184 (060051). ISSN 0094-243X ISBN 9780735419315 (Published) https://doi.org/10.1063/1.5136483 |
| spellingShingle | T Technology (General) TA Engineering (General). Civil engineering (General) Norhayati, Rosli Noor Julailah, Abd Mutalib Noor Amalina Nisa, Ariffin Mazma Syahidatul Ayuni, Mazlan The performance of stochastic Taylor methods and derivative-free method to approximate the solutions of stochastic delay differential equations |
| title | The performance of stochastic Taylor methods and derivative-free method to approximate the solutions of stochastic delay differential equations |
| title_full | The performance of stochastic Taylor methods and derivative-free method to approximate the solutions of stochastic delay differential equations |
| title_fullStr | The performance of stochastic Taylor methods and derivative-free method to approximate the solutions of stochastic delay differential equations |
| title_full_unstemmed | The performance of stochastic Taylor methods and derivative-free method to approximate the solutions of stochastic delay differential equations |
| title_short | The performance of stochastic Taylor methods and derivative-free method to approximate the solutions of stochastic delay differential equations |
| title_sort | performance of stochastic taylor methods and derivative-free method to approximate the solutions of stochastic delay differential equations |
| topic | T Technology (General) TA Engineering (General). Civil engineering (General) |
| url | http://umpir.ump.edu.my/id/eprint/27730/ http://umpir.ump.edu.my/id/eprint/27730/ http://umpir.ump.edu.my/id/eprint/27730/1/The%20performance%20of%20stochastic%20Taylor%20methods%20and%20derivative-free.pdf |